Harmonic Transposition in an Audio Coding Method and System

ABSTRACT

The present invention relates to transposing signals in time and/or frequency and in particular to coding of audio signals. More particular, the present invention relates to high frequency reconstruction (HFR) methods including a frequency domain harmonic transposer. A method and system for generating a transposed output signal from an input signal using a transposition factor T is described. The system comprises an analysis window of length L a , extracting a frame of the input signal, and an analysis transformation unit of order M transforming the samples into M complex coefficients. M is a function of the transposition factor T. The system further comprises a nonlinear processing unit altering the phase of the complex coefficients by using the transposition factor T, a synthesis transformation unit of order M transforming the altered coefficients into M altered samples, and a synthesis window of length L s , generating a frame of the output signal.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of U.S. patentapplication Ser. No. 12/881,821, filed on Sep. 14, 2010, which claimedthe benefit of priority to U.S. Provisional Patent Application Ser. No.61/243,624, filed on Sep. 18, 2009 and PCT Application No.PCT/EP2010/053222, filed Mar. 12, 2010, all of which are herebyincorporated by reference in their entirety.

TECHNICAL FIELD

The present invention relates to transposing signals in frequency and/orstretching/compressing a signal in time and in particular to coding ofaudio signals. In other words, the present invention relates totime-scale and/or frequency-scale modification. More particularly, thepresent invention relates to high frequency reconstruction (HFR) methodsincluding a frequency domain harmonic transposer.

BACKGROUND OF THE INVENTION

HFR technologies, such as the Spectral Band Replication (SBR)technology, allow to significantly improve the coding efficiency oftraditional perceptual audio codecs. In combination with MPEG-4 AdvancedAudio Coding (AAC) it forms a very efficient audio codec, which isalready in use within the XM Satellite Radio system and Digital RadioMondiale, and also standardized within 3GPP, DVD Forum and others. Thecombination of AAC and SBR is called aacPlus. It is part of the MPEG-4standard where it is referred to as the High Efficiency AAC Profile(HE-AAC). In general, HFR technology can be combined with any perceptualaudio codec in a back and forward compatible way, thus offering thepossibility to upgrade already established broadcasting systems like theMPEG Layer-2 used in the Eureka DAB system. HFR transposition methodscan also be combined with speech codecs to allow wide band speech atultra low bit rates.

The basic idea behind HRF is the observation that usually a strongcorrelation between the characteristics of the high frequency range of asignal and the characteristics of the low frequency range of the samesignal is present. Thus, a good approximation for the representation ofthe original input high frequency range of a signal can be achieved by asignal transposition from the low frequency range to the high frequencyrange.

This concept of transposition was established in WO 98/57436 which isincorporated by reference, as a method to recreate a high frequency bandfrom a lower frequency band of an audio signal. A substantial saving inbit-rate can be obtained by using this concept in audio coding and/orspeech coding. In the following, reference will be made to audio coding,but it should be noted that the described methods and systems areequally applicable to speech coding and in unified speech and audiocoding (USAC).

In a HFR based audio coding system, a low bandwidth signal is presentedto a core waveform coder for encoding, and higher frequencies areregenerated at the decoder side using transposition of the low bandwidthsignal and additional side information, which is typically encoded atvery low bit-rates and which describes the target spectral shape. Forlow bit-rates, where the bandwidth of the core coded signal is narrow,it becomes increasingly important to reproduce or synthesize a highband, i.e. the high frequency range of the audio signal, withperceptually pleasant characteristics.

In prior art there are several methods for high frequency reconstructionusing, e.g. harmonic transposition, or time-stretching. One method isbased on phase vocoders operating under the principle of performing afrequency analysis with a sufficiently high frequency resolution. Asignal modification is performed in the frequency domain prior tore-synthesising the signal. The signal modification may be atime-stretch or transposition operation.

One of the underlying problems that exist with these methods are theopposing constraints of an intended high frequency resolution in orderto get a high quality transposition for stationary sounds, and the timeresponse of the system for transient or percussive sounds. In otherwords, while the use of a high frequency resolution is beneficial forthe transposition of stationary signals, such high frequency resolutiontypically requires large window sizes which are detrimental when dealingwith transient portions of a signal. One approach to deal with thisproblem may be to adaptively change the windows of the transposer, e.g.by using window-switching, as a function of input signalcharacteristics. Typically long windows will be used for stationaryportions of a signal, in order to achieve high frequency resolution,while short windows will be used for transient portions of the signal,in order to implement a good transient response, i.e. a good temporalresolution, of the transposer. However, this approach has the drawbackthat signal analysis measures such as transient detection or the likehave to be incorporated into the transposition system. Such signalanalysis measures often involve a decision step, e.g. a decision on thepresence of a transient, which triggers a switching of signalprocessing. Furthermore, such measures typically affect the reliabilityof the system and they may introduce signal artifacts when switching thesignal processing, e.g. when switching between window sizes.

The present invention solves the aforementioned problems regarding thetransient performance of harmonic transposition without the need forwindow switching. Furthermore, improved harmonic transposition isachieved at a low additional complexity.

SUMMARY OF THE INVENTION

The present invention relates to the problem of improved transientperformance for harmonic transposition, as well as assorted improvementsto known methods for harmonic transposition. Furthermore, the presentinvention outlines how additional complexity may be kept at a minimumwhile retaining the proposed improvements.

Among others, the present invention may comprise at least one of thefollowing aspects:

-   -   Oversampling in frequency by a factor being a function of the        transposition factor of the operation point of the transposer;    -   Appropriate choice of the combination of analysis and synthesis        windows; and    -   Ensuring time-alignment of different transposed signals for the        cases where such signals are combined.

According to an aspect of the invention, a system for generating atransposed output signal from an input signal using a transpositionfactor T is described. The transposed output signal may be atime-stretched and/or frequency-shifted version of the input signal.Relative to the input signal, the transposed output signal may bestretched in time by the transposition factor T. Alternatively, thefrequency components of the transposed output signal may be shiftedupwards by the transposition factor T.

The system may comprise an analysis window of length L which extracts Lsamples of the input signal. Typically, the L samples of the inputsignals are samples of the input signal, e.g. an audio signal, in thetime domain. The extracted L samples are referred to as a frame of theinput signal. The system comprises further an analysis transformationunit of order M=F*L transforming the L time-domain samples into Mcomplex coefficients with F being a frequency oversampling factor. The Mcomplex coefficients are typically coefficients in the frequency domain.The analysis transformation may be a Fourier transform, a Fast FourierTransform, a Discrete Fourier Transform, a Wavelet Transform or ananalysis stage of a (possibly modulated) filter bank. The oversamplingfactor F is based on or is a function of the transposition factor T.

The oversampling operation may also be referred to as zero padding ofthe analysis window by additional (F−1)*L zeros. It may also be viewedas choosing a size of an analysis transformation M which is larger thanthe size of the analysis window by a factor F.

The system may also comprise a nonlinear processing unit altering thephase of the complex coefficients by using the transposition factor T.The altering of the phase may comprise multiplying the phase of thecomplex coefficients by the transposition factor T. In addition, thesystem may comprise a synthesis transformation unit of order Mtransforming the altered coefficients into M altered samples and asynthesis window of length L for generating the output signal. Thesynthesis transform may be an inverse Fourier Transform, an inverse FastFourier Transform, an inverse Discrete Fourier Transform, an inverseWavelet Transform, or a synthesis stage of a (possibly) modulated filterbank. Typically, the analysis transform and the synthesis transform arerelated to each other, e.g. in order to achieve perfect reconstructionof an input signal when the transposition factor T=1.

According to another aspect of the invention the oversampling factor Fis proportional to the transposition factor T. In particular, theoversampling factor F may be greater or equal to (T+1)/2. This selectionof the oversampling factor F ensures that undesired signal artifacts,e.g. pre- and post-echoes, which may be incurred by the transpositionare rejected by the synthesis window.

It should be noted that in more general terms, the length of theanalysis window may be L_(a) and the length of the synthesis window maybe L_(s). Also in such cases, it may be beneficial to select the orderof the transformation unit M based on the transposition order T, i.e. asa function of the transposition order T. Furthermore, it may bebeneficial to select M to be greater than the average length of theanalysis window and the synthesis window, i.e. greater than(L_(a)+L_(s))/2. In an embodiment, the difference between the order ofthe transformation unit M and the average window length is proportionalto (T−1). In a further embodiment, M is selected to be greater or equalto (TL_(a)+L_(s))/2. It should be noted that the case where the lengthof the analysis window and the synthesis window is equal, i.e.L_(a)=L_(s)=L, is a special case of the above generic case. For thegeneric case, the oversampling factor F may be

$F \geq {1 + {\left( {T - 1} \right)\frac{L_{a}}{L_{s} + L_{a}}}}$

The system may further comprise an analysis stride unit shifting theanalysis window by an analysis stride of S_(a) samples along the inputsignal. As a result of the analysis stride unit, a succession of framesof the input signal is generated. In addition, the system may comprise asynthesis stride unit shifting the synthesis window and/or successiveframes of the output signal by a synthesis stride of S_(s) samples. As aresult, a succession of shifted frames of the output signal is generatedwhich may be overlapped and added in an overlap-add unit.

In other words, the analysis window may extract or isolate L or moregenerally L_(a) samples of the input signal, e.g. by multiplying a setof L samples of the input signal with non-zero window coefficients. Sucha set of L samples may be referred to as an input signal frame or as aframe of the input signal. The analysis stride unit shifts the analysiswindow along the input signal and thereby selects a different frame ofthe input signal, i.e. it generates a sequence of frames of the inputsignal. The sample distance between successive frames is given by theanalysis stride. In a similar manner, the synthesis stride unit shiftsthe synthesis window and/or the frames of the output signal, i.e. itgenerates a sequence of shifted frames of the output signal. The sampledistance between successive frames of the output signal is given by thesynthesis stride. The output signal may be determined by overlapping thesequence of frames of the output signal and by adding sample valueswhich coincide in time.

According to a further aspect of the invention, the synthesis stride isT times the analysis stride. In such cases, the output signalcorresponds to the input signal, time-stretched by the transpositionfactor T. In other words, by selecting the synthesis stride to be Ttimes greater than the analysis stride, a time shift or time stretch ofthe output signal with regards to the input signal may be obtained. Thistime shift is of order T.

In other words, the above mentioned system may be described as follows:Using an analysis window unit, an analysis transformation unit and ananalysis stride unit with an analysis stride S_(a), a suite or sequenceof sets of M complex coefficients may be determined from an inputsignal. The analysis stride defines the number of samples that theanalysis window is moved forward along the input signal. As the elapsedtime between two successive samples is given by the sampling rate, theanalysis stride also defines the elapsed time between two frames of theinput signal. By consequences, also the elapsed time between twosuccessive sets of M complex coefficients is given by the analysisstride S_(a).

After passing the nonlinear processing unit where the phase of thecomplex coefficients may be altered, e.g. by multiplying it with thetransposition factor T, the suite or sequence of sets of M complexcoefficients may be re-converted into the time-domain. Each set of Maltered complex coefficients may be transformed into M altered samplesusing the synthesis transformation unit. In a following overlap-addoperation involving the synthesis window unit and the synthesis strideunit with a synthesis stride S_(s), the suite of sets of M alteredsamples may be overlapped and added to form the output signal. In thisoverlap-add operation, successive sets of M altered samples may beshifted by S_(s) samples with respect to one another, before they may bemultiplied with the synthesis window and subsequently added to yield theoutput signal. Consequently, if the synthesis stride S_(s) is T timesthe analysis stride S_(a), the signal may be time stretched by a factorT.

According to a further aspect of the invention, the synthesis window isderived from the analysis window and the synthesis stride. Inparticular, the synthesis window may be given by the formula:

${{v_{s}(n)} = {{v_{a}(n)}\left( {\sum\limits_{k = {- \infty}}^{\infty}\; \left( {v_{a}\left( {n - {{k \cdot \Delta}\; t}} \right)} \right)^{2}} \right)^{- 1}}},$

with v_(s)(n) being the synthesis window, v_(a)(n) being the analysiswindow, and Δt being the synthesis stride S_(s). The analysis and/orsynthesis window may be one of a Gaussian window, a cosine window, aHamming window, a Hann window, a rectangular window, a Bartlett windows,a Blackman windows, a window having the function

${{v(n)} = {\sin \left( {\frac{\pi}{L}\left( {n + 0.5} \right)} \right)}},{0 \leq n < L},$

wherein in the case of different lengths of the analysis window and thesynthesis window, L may be L_(a) or L_(s), respectively.

According to another aspect of the invention, the system furthercomprises a contraction unit performing e.g. a rate conversion of theoutput signal by the transposition order T, thereby yielding atransposed output signal. By selecting the synthesis stride to be Ttimes the analysis stride, a time-stretched output signal may beobtained as outlined above. If the sampling rate of the time-stretchedsignal is increased by a factor T or if the time-stretched signal isdown-sampled by a factor T, a transposed output signal may be generatedthat corresponds to the input signal, frequency-shifted by thetransposition factor T. The downsampling operation may comprise the stepof selecting only a subset of samples of the output signal.

Typically, only every T^(th) sample of the output signal is retained.Alternatively, the sampling rate may be increased by a factor T, i.e.the sampling rate is interpreted as being T times higher. In otherwords, re-sampling or sampling rate conversion means that the samplingrate is changed, either to a higher or a lower value. Downsampling meansrate conversion to a lower value.

According to a further aspect of the invention, the system may generatea second output signal from the input signal. The system may comprise asecond nonlinear processing unit altering the phase of the complexcoefficients by using a second transposition factor T₂ and a secondsynthesis stride unit shifting the synthesis window and/or the frames ofthe second output signal by a second synthesis stride. Altering of thephase may comprise multiplying the phase by a factor T₂. By altering thephase of the complex coefficients using the second transposition factorand by transforming the second altered coefficients into M secondaltered samples and by applying the synthesis window, frames of thesecond output signal may be generated from a frame of the input signal.By applying the second synthesis stride to the sequence of frames of thesecond output signal, the second output signal may be generated in theoverlap-add unit.

The second output signal may be contracted in a second contracting unitperforming e.g. a rate conversion of the second output signal by thesecond transposition order T₂. This yields a second transposed outputsignal. In summary, a first transposed output signal can be generatedusing the first transposition factor T and a second transposed outputsignal can be generated using the second transposition factor T₂. Thesetwo transposed output signals may then be merged in a combining unit toyield the overall transposed output signal. The merging operation maycomprise adding of the two transposed output signals. Such generationand combining of a plurality of transposed output signals may bebeneficial to obtain good approximations of the high frequency signalcomponent which is to be synthesized. It should be noted that any numberof transposed output signals may be generated using a plurality oftransposition orders. This plurality of transposed outputs signals maythen be merged, e.g. added, in a combining unit to yield an overalltransposed output signal.

It may be beneficial that the combining unit weights the first andsecond transposed output signals prior to merging. The weighting may beperformed such that the energy or the energy per bandwidth of the firstand second transposed output signals corresponds to the energy or energyper bandwidth of the input signal, respectively.

According to a further aspect of the invention, the system may comprisean alignment unit which applies a time offset to the first and secondtransposed output signals prior to entering the combining unit. Suchtime offset may comprise the shifting of the two transposed outputsignals with respect to one another in the time domain. The time offsetmay be a function of the transposition order and/or the length of thewindows. In particular, the time offset may be determined as

$\frac{\left( {T - 2} \right)L}{4}.$

According to another aspect of the invention, the above describedtransposition system may be embedded into a system for decoding areceived multimedia signal comprising an audio signal. The decodingsystem may comprise a transposition unit which corresponds to the systemoutlined above, wherein the input signal typically is a low frequencycomponent of the audio signal and the output signal is a high frequencycomponent of the audio signal. In other words, the input signaltypically is a low pass signal with a certain bandwidth and the outputsignal is a bandpass signal of typically a higher bandwidth.Furthermore, it may comprise a core decoder for decoding the lowfrequency component of the audio signal from the received bitstream.Such core decoder may be based on a coding scheme such as Dolby E, DolbyDigital or AAC. In particular, such decoding system may be a set-top boxfor decoding a received multimedia signal comprising an audio signal andother signals such as video.

It should be noted that the present invention also describes a methodfor transposing an input signal by a transposition factor T. The methodcorresponds to the system outlined above and may comprise anycombination of the above mentioned aspects. It may comprise the steps ofextracting samples of the input signal using an analysis window oflength L, and of selecting an oversampling factor F as a function of thetransposition factor T. It may further comprise the steps oftransforming the L samples from the time domain into the frequencydomain yielding F*L complex coefficients, and of altering the phase ofthe complex coefficients with the transposition factor T. In additionalsteps, the method may transform the F*L altered complex coefficientsinto the time domain yielding F*L altered samples, and it may generatethe output signal using a synthesis window of length L. It should benoted that the method may also be adapted to general lengths of theanalysis and synthesis window, i.e. to general L_(a) and L_(s), atoutlined above.

According to a further aspect of the invention, the method may comprisethe steps of shifting the analysis window by an analysis stride of S_(a)samples along the input signal, and/or by shifting the synthesis windowand/or the frames of the output signal by a synthesis stride of S_(s)samples. By selecting the synthesis stride to be T times the analysisstride, the output signal may be time-stretched with respect to theinput signal by a factor T. When executing an additional step ofperforming a rate conversion of the output signal by the transpositionorder T, a transposed output signal may be obtained. Such transposedoutput signal may comprise frequency components that are upshifted by afactor T with respect to the corresponding frequency components of theinput signal.

The method may further comprise steps for generating a second outputsignal. This may be implemented by altering the phase of the complexcoefficients by using a second transposition factor T₂, by shifting thesynthesis window and/or the frames of the second output signal by asecond synthesis stride a second output signal may be generated usingthe second transposition factor T₂ and the second synthesis stride. Byperforming a rate conversion of the second output signal by the secondtransposition order T₂, a second transposed output signal may begenerated. Eventually, by merging the first and second transposed outputsignals a merged or overall transposed output signal including highfrequency signal components generated by two or more transpositions withdifferent transposition factors may be obtained.

According to other aspects of the invention, the invention describes asoftware program adapted for execution on a processor and for performingthe method steps of the present invention when carried out on acomputing device. The invention also describes a storage mediumcomprising a software program adapted for execution on a processor andfor performing the method steps of the invention when carried out on acomputing device. Furthermore, the invention describes a computerprogram product comprising executable instructions for performing themethod of the invention when executed on a computer.

According to a further aspect, another method and system for transposingan input signal by a transposition factor T is described. This methodand system may be used standalone or in combination with the methods andsystems outlined above. Any of the features outlined in the presentdocument may be applied to this method/system and vice versa.

The method may comprise the step of extracting a frame of samples of theinput signal using an analysis window of length L. Then, the frame ofthe input signal may be transformed from the time domain into thefrequency domain yielding M complex coefficients. The phase of thecomplex coefficients may be altered with the transposition factor T andthe M altered complex coefficients may be transformed into the timedomain yielding M altered samples. Eventually, a frame of an outputsignal may be generated using a synthesis window of length L. The methodand system may use an analysis window and a synthesis window which aredifferent from each other. The analysis and the synthesis window may bedifferent with regards to their shape, their length, the number ofcoefficients defining the windows and/or the values of the coefficientsdefining the windows. By doing this, additional degrees of freedom inthe selection of the analysis and synthesis windows may be obtained suchthat aliasing of the transposed output signal may be reduced or removed.

According to another aspect, the analysis window and the synthesiswindow are bi-orthogonal with respect to one another. The synthesiswindow v_(s)(n) may be given by:

${{v_{s}(n)} = {c\frac{v_{a}(n)}{{s\left( {n\left( {{mod}{\; \;}\Delta \; t_{s}} \right)} \right)}\;}}},{0 < L},$

with c being a constant, v_(a)(n) being the analysis window (311),Δt_(s) being a time-stride of the synthesis window and s(n) being givenby:

${{s(m)} = {\sum\limits_{i = 0}^{{Ll}{({{\Delta \; t_{s}} - 1})}}\; {v_{a}^{2}\left( {m + {\Delta \; t_{s}i}} \right)}}},{0 \leq m < {\Delta \; {t_{s}.}}}$

The time stride of the synthesis window Δt_(s) typically corresponds tothe synthesis stride S_(s).

According to a further aspect, the analysis window may be selected suchthat its z transform has dual zeros on the unit circle. Preferably, thez transform of the analysis window only has dual zeros on the unitcircle. By way of example, the analysis window may be a squared sinewindow. In another example, the analysis window of length L may bedetermined by convolving two sine windows of length L, yielding asquared sine window of length 2L−1. In a further step a zero is appendedto the squared sine window, yielding a base window of length 2L.Eventually, the base window may be resampled using linear interpolation,thereby yielding an even symmetric window of length L as the analysiswindow.

The methods and systems described in the present document may beimplemented as software, firmware and/or hardware. Certain componentsmay e.g. be implemented as software running on a digital signalprocessor or microprocessor. Other component may e.g. be implemented ashardware and or as application specific integrated circuits. The signalsencountered in the described methods and systems may be stored on mediasuch as random access memory or optical storage media. They may betransferred via networks, such as radio networks, satellite networks,wireless networks or wireline networks, e.g. the internet. Typicaldevices making use of the method and system described in the presentdocument are set-top boxes or other customer premises equipment whichdecode audio signals. On the encoding side, the method and system may beused in broadcasting stations, e.g. in video or TV head end systems.

It should be noted that the embodiments and aspects of the inventiondescribed in this document may be arbitrarily combined. In particular,it should be noted that the aspects outlined for a system are alsoapplicable to the corresponding method embraced by the presentinvention. Furthermore, it should be noted that the disclosure of theinvention also covers other claim combinations than the claimcombinations which are explicitly given by the back references in thedependent claims, i.e., the claims and their technical features can becombined in any order and any formation.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will now be described by way of illustrativeexamples, not limiting the scope or spirit of the invention, withreference to the accompanying drawings, in which:

FIG. 1 illustrates a Dirac at a particular position as it appears in theanalysis and synthesis windows of a harmonic transposer;

FIG. 2 illustrates a Dirac at a different position as it appears in theanalysis and synthesis windows of a harmonic transposer;

FIG. 3 illustrates a Dirac for the position of FIG. 2 as it will appearaccording to the present invention;

FIG. 4 illustrates the operation of an HFR enhanced audio decoder;

FIG. 5 illustrates the operation of a harmonic transposer using severalorders;

FIG. 6 illustrates the operation of a frequency domain (FD) harmonictransposer

FIG. 7 shows a succession of analysis synthesis windows;

FIG. 8 illustrates analysis and synthesis windows at different strides;

FIG. 9 illustrates the effect of the re-sampling on the synthesis strideof windows;

FIGS. 10 and 11 illustrate embodiments of an encoder and a decoder,respectively, using the enhanced harmonic transposition schemes outlinedin the present document; and

FIG. 12 illustrates an embodiment of a transposition unit shown in FIGS.10 and 11.

DETAILED DESCRIPTION

The below-described embodiments are merely illustrative for theprinciples of the present invention for Improved Harmonic Transposition.It is understood that modifications and variations of the arrangementsand the details described herein will be apparent to others skilled inthe art. It is the intent, therefore, to be limited only by the scope ofthe impending patent claims and not by the specific details presented byway of description and explanation of the embodiments herein.

In the following, the principle of harmonic transposition in thefrequency domain and the proposed improvements as taught by the presentinvention are outlined. A key component of the harmonic transposition istime stretching by an integer transposition factor T which preserves thefrequency of sinusoids. In other words, the harmonic transposition isbased on time stretching of the underlying signal by a factor T. Thetime stretching is performed such that frequencies of sinusoids whichcompose the input signal are maintained. Such time stretching may beperformed using a phase vocoder. The phase vocoder is based on afrequency domain representation furnished by a windowed DFT filter bankwith analysis window v_(a)(n) and synthesis window v_(s)(n). Suchanalysis/synthesis transform is also referred to as short-time FourierTransform (STFT).

A short-time Fourier transform is performed on a time-domain inputsignal to obtain a succession of overlapped spectral frames. In order tominimize possible side-band effects, appropriate analysis/synthesiswindows, e.g. Gaussian windows, cosine windows, Hamming windows, Hannwindows, rectangular windows, Bartlett windows, Blackman windows, andothers, should be selected. The time delay at which every spectral frameis picked up from the input signal is referred to as the hop size orstride. The STFT of the input signal is referred to as the analysisstage and leads to a frequency domain representation of the inputsignal. The frequency domain representation comprises a plurality ofsubband signals, wherein each subband signal represents a certainfrequency component of the input signal.

The frequency domain representation of the input signal may then beprocessed in a desired way. For the purpose of time-stretching of theinput signal, each subband signal may be time-stretched, e.g. bydelaying the subband signal samples. This may be achieved by using asynthesis hop-size which is greater than the analysis hop-size. The timedomain signal may be rebuilt by performing an inverse (Fast) Fouriertransform on all frames followed by a successive accumulation of theframes. This operation of the synthesis stage is referred to asoverlap-add operation. The resulting output signal is a time-stretchedversion of the input signal comprising the same frequency components asthe input signal. In other words, the resulting output signal has thesame spectral composition as the input signal, but it is slower than theinput signal i.e. its progression is stretched in time.

The transposition to higher frequencies may then be obtainedsubsequently, or in an integrated manner, through downsampling of thestretched signals. As a result the transposed signal has the length intime of the initial signal, but comprises frequency components which areshifted upwards by a pre-defined transposition factor.

In mathematical terms, the phase vocoder may be described as follows. Aninput signal x(t) is sampled at a sampling rate R to yield the discreteinput signal x(n). During the analysis stage, a STFT is determined forthe input signal x(n) at particular analysis time instants t_(a) ^(k)for successive values k. The analysis time instants are preferablyselected uniformly through t_(a) ^(k)=k·Δt_(a), where Δt_(a) is theanalysis hop factor or analysis stride. At each of these analysis timeinstants t_(a) ^(k), a Fourier transform is calculated over a windowedportion of the original signal x(n), wherein the analysis windowv_(a)(t) is centered around t_(a) ^(k), i.e. v_(a)(t−t_(a) ^(k)). Thiswindowed portion of the input signal x(n) is referred to as a frame. Theresult is the STFT representation of the input signal x(n), which may bedenoted as:

${{X\left( {t_{a}^{k},\Omega_{m}} \right)} = {\sum\limits_{n = {- \infty}}^{\infty}\; {{v_{a}\left( {n - t_{a}^{k}} \right)}{x(n)}{\exp \left( {{- j}\; \Omega_{m}n} \right)}}}},$

where

$\Omega_{m} = {2\pi \frac{m}{M}}$

is the center frequency of the m^(th) subband signal of the STFTanalysis and M is the size of the discrete Fourier transform (DFT). Inpractice, the window function v_(a)(n) has a limited time span, i.e. itcovers only a limited number of samples L, which is typically equal tothe size M of the DFT. By consequence, the above sum has a finite numberof terms. The subband signals X(t_(a) ^(k),Ω_(m)) are both a function oftime, via index k, and frequency, via the subband center frequencyΩ_(m).

The synthesis stage may be performed at synthesis time instants t_(s)^(k) which are typically uniformly distributed according to t_(s)^(k)=k·Δt_(s), where Δt_(s) is the synthesis hop factor or synthesisstride. At each of these synthesis time instants, a short-time signaly_(k)(n) is obtained by inverse-Fourier-transforming the STFT subbandsignal Y(t_(s) ^(k),Ω_(m)), which may be identical to X (t_(a)^(k),Ω_(m)), at the synthesis time instants t_(s) ^(k). However,typically the STFT subband signals are modified, e.g. time-stretchedand/or phase modulated and/or amplitude modulated, such that theanalysis subband signal X(t_(a) ^(k),Ω_(m)) differs from the synthesissubband signal Y(t_(s) ^(k),Ω_(m)). In a preferred embodiment, the STFTsubband signals are phase modulated, i.e. the phase of the STFT subbandsignals is modified. The short-term synthesis signal y_(k)(n) can bedenoted as

${y_{k}(n)} = {\frac{1}{M}{\sum\limits_{m = 0}^{M - 1}{{Y\left( {t_{s}^{k},\Omega_{m}} \right)}{{\exp \left( {j\; \Omega_{m}n} \right)}.}}}}$

The short-term signal y_(k)(n) may be viewed as a component of theoverall output signal y(n) comprising the synthesis subband signalsY(t_(s) ^(k),Ω_(m)) for m=0, . . . , M−1, at the synthesis time instantt_(s) ^(k). I.e. the short-term signal y_(k)(n) is the inverse DFT for aspecific signal frame. The overall output signal y(n) can be obtained byoverlapping and adding windowed short-time signals y_(k)(n) at allsynthesis time instants t_(s) ^(k). I.e. the output signal y(n) may bedenoted as

${{y(n)} = {\sum\limits_{k = {- \infty}}^{\infty}{{v_{s}\left( {n - t_{s}^{k}} \right)}{y_{k}\left( {n - t_{s}^{k}} \right)}}}},$

where v_(s)(n−t_(s) ^(k)) is the synthesis window centered around thesynthesis time instant t_(s) ^(k). It should be noted that the synthesiswindow typically has a limited number of samples L, such that the abovementioned sum only comprises a limited number of terms.

In the following, the implementation of time-stretching in the frequencydomain is outlined. A suitable starting point in order to describeaspects of the time stretcher is to consider the case T=1, i.e. the casewhere the transposition factor T equals 1 and where no stretchingoccurs. Assuming the analysis time stride Δt_(a) and the synthesis timestride Δt_(s) of the DFT filter bank to be equal, i.e. Δt_(a)=Δt_(s)=Δt,the combined effect of analysis followed by synthesis is that of anamplitude modulation with the Δt-periodic function

$\begin{matrix}{{{K(n)} = {\sum\limits_{k = {- \infty}}^{\infty}{q\left( {n - {k\; \Delta \; t}} \right)}}},} & (1)\end{matrix}$

where q(n)=v_(a)(n)v_(s)(n) is the point-wise product of the twowindows, i.e. the point-wise product of the analysis window and thesynthesis window. It is advantageous to choose the windows such thatK(n)=1 or another constant value, since then the windowed DFT filterbank achieves perfect reconstruction. If the analysis window v_(a)(n) isgiven, and if the analysis window is of sufficiently long durationcompared to the stride Δt, one can obtain perfect reconstruction bychoosing the synthesis window according to

$\begin{matrix}{{v_{s}(n)} = {{v_{a}(n)}{\left( {\sum\limits_{k = {- \infty}}^{\infty}\left( {v_{a}\left( {n - {{k \cdot \Delta}\; t}} \right)} \right)^{2}} \right)^{- 1}.}}} & (2)\end{matrix}$

For T>1, i.e. for a transposition factor greater than 1, a time stretchmay be obtained by performing the analysis at stride

${\Delta \; t_{a}} = \frac{\Delta \; t}{T}$

whereas the synthesis stride is maintained at Δt_(s)=Δt. In other words,a time stretch by a factor T may be obtained by applying a hop factor orstride at the analysis stage which is T times smaller than the hopfactor or stride at the synthesis stage. As can be seen from theformulas provided above, the use of a synthesis stride which is T timesgreater than the analysis stride will shift the short-term synthesissignals y_(k)(n) by T times greater intervals in the overlap-addoperation. This will eventually result in a time-stretch of the outputsignal y(n).

It should be noted that the time stretch by the factor T may furtherinvolve a phase multiplication by a factor T between the analysis andthe synthesis. In other words, time stretching by a factor T involvesphase multiplication by a factor T of the subband signals.

In the following it is outlined how the above described time-stretchingoperation may be translated into a harmonic transposition operation. Thepitch-scale modification or harmonic transposition may be obtained byperforming a sample-rate conversion of the time stretched output signaly(n). For performing a harmonic transposition by a factor T, an outputsignal y(n) which is a time-stretched version by the factor T of theinput signal x(n) may be obtained using the above described phasevocoding method. The harmonic transposition may then be obtained bydownsampling the output signal y(n) by a factor T or by converting thesampling rate from R to TR. In other words, instead of interpreting theoutput signal y(n) as having the same sampling rate as the input signalx(n) but of T times duration, the output signal y(n) may be interpretedas being of the same duration but of T times the sampling rate. Thesubsequent downsampling of T may then be interpreted as making theoutput sampling rate equal to the input sampling rate so that thesignals eventually may be added. During these operations, care should betaken when downsampling the transposed signal so that no aliasingoccurs.

When assuming the input signal x(n) to be a sinusoid and when assuming asymmetric analysis windows v_(a)(n), the method of time stretching basedon the above described phase vocoder will work perfectly for odd valuesof T, and it will result in a time stretched version of the input signalx(n) having the same frequency. In combination with a subsequentdownsampling, a sinusoid y(n) with a frequency which is T times thefrequency of the input signal x(n) will be obtained.

For even values of T, the time stretching/harmonic transposition methodoutlined above will be more approximate, since negative valued sidelobes of the frequency response of the analysis window v_(a)(n) will bereproduced with different fidelity by the phase multiplication. Thenegative side lobes typically come from the fact that most practicalwindows (or prototype filters) have numerous discrete zeros located onthe unit circle, resulting in 180 degree phase shifts. When multiplyingthe phase angles using even transposition factors the phase shifts aretypically translated to 0 (or rather multiples of 360) degrees dependingon the transposition factor used. In other words, when using eventransposition factors, the phase shifts vanish. This will typically giverise to aliasing in the transposed output signal y(n). A particularlydisadvantageous scenario may arise when a sinusoidal is located in afrequency corresponding to the top of the first side lobe of theanalysis filter. Depending on the rejection of this lobe in themagnitude response, the aliasing will be more or less audible in theoutput signal. It should be noted that, for even factors T, decreasingthe overall stride Δt typically improves the performance of the timestretcher at the expense of a higher computational complexity.

In EP0940015B1/WO98/57436 entitled “Source coding enhancement usingspectral band replication” which is incorporated by reference, a methodhas been described on how to avoid aliasing emerging from a harmonictransposer when using even transposition factors. This method, calledrelative phase locking, assesses the relative phase difference betweenadjacent channels, and determines whether a sinusoidal is phase invertedin either channel. The detection is performed by using equation (32) ofEP0940015B1. The channels detected as phase inverted are corrected afterthe phase angles are multiplied with the actual transposition factor.

In the following a novel method for avoiding aliasing when using evenand/or odd transposition factors T is described. In contrary to therelative phase locking method of EP0940015B1, this method does notrequire the detection and correction of phase angles. The novel solutionto the above problem makes use of analysis and synthesis transformwindows that are not identical. In the perfect reconstruction (PR) case,this corresponds to a bi-orthogonal transform/filter bank rather than anorthogonal transform/filter bank.

To obtain a bi-orthogonal transform given a certain analysis windowv_(a)(n), the synthesis window v_(s)(n) is chosen to follow

${{\sum\limits_{i = 0}^{L/{({{\Delta \; t_{s}} - 1})}}{{v_{a}\left( {m + {\Delta \; t_{s}i}} \right)}{v_{s}\left( {m + {\Delta \; t_{s}i}} \right)}}} = c},{0 \leq m < {\Delta \; t_{s}}}$

where c is a constant, Δt_(s) is the synthesis time stride and L is thewindow length. If the sequence s(n) is defined as

${{s(m)} = {\sum\limits_{i = 0}^{L/{({{\Delta \; t_{s}} - 1})}}{v_{a}^{2}\left( {m + {\Delta \; t_{s}i}} \right)}}},{0 \leq m < {\Delta \; t_{s}}},$

i.e. v_(a)(n)=v_(s)(n) is used for both analysis and synthesiswindowing, then the condition for an orthogonal transform is

s(m)=c, 0≦m<Δt _(s).

However, in the following another sequence w(n) is introduced, whereinw(n) is a measure on how much the synthesis window v_(s)(n) deviatesfrom the analysis window v_(a)(n), i.e. how much the bi-orthogonaltransform differs from the orthogonal case. The sequence w(n) is givenby

${{w(n)} = \frac{v_{s}(n)}{v_{a}(n)}},{0 \leq n < {L.}}$

The condition for perfect reconstruction is then given by

${{\sum\limits_{i = 0}^{L/{({{\Delta \; t_{s}} - 1})}}{{v_{a}^{2}\left( {m + {\Delta \; t_{s}i}} \right)}{w\left( {m + {\Delta \; t_{s}i}} \right)}}} = c},{0 \leq m < {\Delta \; t_{s}}},$

For a possible solution, w(n) could be restricted to be periodic withthe synthesis time stride Δt_(s), i.e. w(n)=w(n+Δt_(s)i), ∀i,n. Then,one obtains

${{\sum\limits_{i = 0}^{L/{({{\Delta \; t_{s}} - 1})}}{{v_{a}^{2}\left( {m + {\Delta \; t_{s}i}} \right)}w\left( {m + {\Delta \; t_{s}i}} \right)}} = {{{w(m)}{\sum\limits_{i = 0}^{L/{({{\Delta \; t_{s}} - 1})}}{v_{a}^{2}\left( {m + {\Delta \; t_{s}i}} \right)}}} = {{{w(m)}{s(m)}} = c}}},{0 \leq m < {\Delta \; {t_{s}.}}}$

The condition on the synthesis window v_(s)(n) is hence

${{v_{s}(n)} = {{{w\left( {n\left( {{mod}\; \Delta \; t_{s}} \right)} \right)}{v_{a}(n)}} = {c\frac{v_{a}(n)}{s\left( {n\left( {{mod}\; \Delta \; t_{s}} \right)} \right)}}}},{0 \leq n < {L.}}$

By deriving the synthesis windows v_(s)(n) as outlined above, a muchlarger freedom when designing the analysis window v_(a)(n) is provided.This additional freedom may be used to design a pair ofanalysis/synthesis windows which does not exhibit aliasing of thetransposed signal.

To obtain an analysis/synthesis window pair that suppresses aliasing foreven transposition factors, several embodiments will be outlined in thefollowing. According to a first embodiment the windows or prototypefilters are made long enough to attenuate the level of the first sidelobe in the frequency response below a certain “aliasing” level. Theanalysis time stride Δt_(a) will in this case only be a (small) fractionof the window length L. This typically results in smearing oftransients, e.g. in percussive signals.

According to a second embodiment, the analysis window v_(a)(n) is chosento have dual zeros on the unit circle. The phase response resulting froma dual zero is a 360 degree phase shift. These phase shifts are retainedwhen the phase angles are multiplied with the transposition factors,regardless if the transposition factors are odd or even. When a properand smooth analysis filter v_(a)(n), having dual zeros on the unitcircle, is obtained, the synthesis window is obtained from the equationsoutlined above.

In an example of the second embodiment, the analysis filter/windowv_(a)(n) is the “squared sine window”, i.e. the sine window

${{v(n)} = {\sin \left( {\frac{\pi}{L}\left( {n + 0.5} \right)} \right)}},{0 \leq n < L}$

convolved with itself as v_(a)(n)=v(n)

v(n). However, it should be noted that the resulting filter/windowv_(a)(n) will be odd symmetric with length L_(a)=2L−1, i.e. an oddnumber of filter/window coefficients. When a filter/window with an evenlength is more appropriate, in particular an even symmetric filter, thefilter may be obtained by first convolving two sine windows of length L.Then, a zero is appended to the end of the resulting filter.Subsequently, the 2L long filter is resampled using linear interpolationto a length L even symmetric filter, which still has dual zeros only onthe unit circle.

Overall, it has been outlined, how a pair of analysis and synthesiswindows may be selected such that aliasing in the transposed outputsignal may be avoided or significantly reduced. The method isparticularly relevant when using even transposition factors.

Another aspect to consider in the context of vocoder based harmonictransposers is phase unwrapping. It should be noted that whereas greatcare has to be taken related to phase unwrapping issues in generalpurpose phase vocoders, the harmonic transposer has unambiguouslydefined phase operations when integer transposition factors T are used.Thus, in preferred embodiments the transposition order T is an integervalue. Otherwise, phase unwrapping techniques could be applied, whereinphase unwrapping is a process whereby the phase increment between twoconsecutive frames is used to estimate the instantaneous frequency of anearby sinusoid in each channel.

Yet another aspect to consider, when dealing with the transposition ofaudio and/or voice signals, is the processing of stationary and/ortransient signal sections. Typically, in order to be able to transposestationary audio signals without intermodulation artifacts, thefrequency resolution of the DFT filter bank has to be rather high, andtherefore the windows are long compared to transients in the inputsignals x(n), notably audio and/or voice signals. As a result, thetransposer has a poor transient response. However, as will be describedin the following, this problem can be solved by a modification of thewindow design, the transform size and the time stride parameters. Hence,unlike many state of the art methods for phase vocoder transientresponse enhancement, the proposed solution does not rely on any signaladaptive operation such as transient detection.

In the following, the harmonic transposition of transient signals usingvocoders is outlined. As a starting point, a prototype transient signal,a discrete time Dirac pulse at time instant t=t₀,

${\delta \left( {t - t_{0}} \right)} = \left\{ {\begin{matrix}{1,{t = t_{0}}} \\{0,{t \neq t_{0}}}\end{matrix},} \right.$

is considered. The Fourier transform of such a Dirac pulse has unitmagnitude and a linear phase with a slope proportional to t₀:

${X\left( \Omega_{m} \right)} = {{\sum\limits_{n = {- \infty}}^{\infty}{{\delta \left( {n - t_{0}} \right)}{\exp \left( {{- j}\; \Omega_{m}n} \right)}}} = {{\exp \left( {{- j}\; \Omega_{m}t_{0}} \right)}.}}$

Such Fourier transform can be considered as the analysis stage of thephase vocoder described above, wherein a flat analysis window v_(a)(n)of infinite duration is used. In order to generate an output signal y(n)which is time-stretched by a factor T, i.e. a Dirac pulse δ(t−Tt₀) atthe time instant t=Tt₀, the phase of the analysis subband signals shouldbe multiplied by the factor T in order to obtain the synthesis subbandsignal Y(Ω_(m))=exp(−jΩ_(m)Tt₀) which yields the desired Dirac pulseδ(t−Tt₀) as an output of an inverse Fourier Transform.

This shows that the operation of phase multiplication of the analysissubband signals by a factor T leads to the desired time-shift of a Diracpulse, i.e. of a transient input signal. It should be noted that formore realistic transient signals comprising more than one non-zerosample, the further operations of time-stretching of the analysissubband signals by a factor T should be performed. In other words,different hop sizes should be used at the analysis and the synthesisside.

However, it should be noted that the above considerations refer to ananalysis/synthesis stage using analysis and synthesis windows ofinfinite lengths. Indeed, a theoretical transposer with a window ofinfinite duration would give the correct stretch of a Dirac pulseδ(t−t₀). For a finite duration windowed analysis, the situation isscrambled by the fact that each analysis block is to be interpreted asone period interval of a periodic signal with period equal to the sizeof the DFT.

This is illustrated in FIG. 1 which shows the analysis and synthesis 100of a Dirac pulse δ(t−t₀). The upper part of FIG. 1 shows the input tothe analysis stage 110 and the lower part of FIG. 1 shows the output ofthe synthesis stage 120. The upper and lower graphs represent the timedomain. The stylized analysis window 111 and synthesis window 121 aredepicted as triangular (Bartlett) windows. The input pulse δ(t−t₀) 112at time instant t=t₀ is depicted on the top graph 110 as a verticalarrow. It is assumed that the DFT transform block is of size M=L, i.e.the size of the DFT transform is chosen to be equal to the size of thewindows. The phase multiplication of the subband signals by the factor Twill produce the DFT analysis of a Dirac pulse δ(t−Tt₀) at t=Tt₀,however, periodized to a Dirac pulse train with period L. This is due tothe finite length of the applied window and Fourier Transform. Theperiodized pulse train with period L is depicted by the dashed arrows123, 124 on the lower graph.

In a real-world system, where both the analysis and synthesis windowsare of finite length, the pulse train actually contains a few pulsesonly (depending on the transposition factor), one main pulse, i.e. thewanted term, a few pre-pulses and a few post-pulses, i.e. the unwantedterms. The pre- and post-pulses emerge because the DFT is periodic (withL). When a pulse is located within an analysis window, so that thecomplex phase gets wrapped when multiplied by T (i.e. the pulse isshifted outside the end of the window and wraps back to the beginning),an unwanted pulse emerges. The unwanted pulses may have, or may nothave, the same polarity as the input pulse, depending on the location inthe analysis window and the transposition factor.

This can be seen mathematically when transforming the Dirac pulseδ(t−t₀) situated in the interval −L/2≦t₀<L/2 using a DFT with length Lcentered around t=0,

${X\left( \Omega_{m} \right)} = {{\sum\limits_{n = {{- L}/2}}^{{L/2} - 1}\; {{\delta \left( {n - t_{0}} \right)}{\exp \left( {{- {j\Omega}_{m}}n} \right)}}} = {{\exp \left( {{- {j\Omega}_{m}}t_{0}} \right)}.}}$

The analysis subband signals are phase multiplied with a factor T toobtain the synthesis subband signals Y(Ω_(m))=exp(−jΩ_(m)Tt₀). Then theinverse DFT is applied to obtain the periodic synthesis signal:

${y(n)} = {{\frac{1}{L}{\sum\limits_{m = {{- L}/2}}^{{L/2} - 1}\; {{\exp \left( {{- {j\Omega}_{m}}{Tt}_{0}} \right)}{\exp \left( {{j\Omega}_{m}n} \right)}}}} = {\sum\limits_{k = {- \infty}}^{\infty}\; {{\delta \left( {n - {Tt}_{0} + {kL}} \right)}.}}}$

i.e. a Dirac pulse train with period L.

In the example of FIG. 1, the synthesis windowing uses a finite windowv_(s)(n) 121. The finite synthesis window 121 picks the desired pulseδ(t−Tt₀) at t=Tt₀ which is depicted as a solid arrow 122 and cancels theother contributions which are shown as dashed arrows 123, 124.

As the analysis and synthesis stage move along the time axis accordingto the hop factor or time stride Δt, the pulse δ(t−t₀) 112 will haveanother position relative to the center of the respective analysiswindow 111. As outlined above, the operation to achieve time-stretchingconsists in moving the pulse 112 to T times its position relative to thecenter of the window. As long as this position is within the window 121,this time-stretch operation guarantees that all contributions add up toa single time stretched synthesized pulse δ(t−Tt₀) at t=Tt₀.

However, a problem occurs for the situation of FIG. 2, where the pulseδ(t−t₀) 212 moves further out towards the edge of the DFT block. FIG. 2illustrates a similar analysis/synthesis configuration 200 as FIG. 1.The upper graph 210 shows the input to the analysis stage and theanalysis window 211, and the lower graph 220 illustrates the output ofthe synthesis stage and the synthesis window 221. When time-stretchingthe input Dirac pulse 212 by a factor T, the time stretched Dirac pulse222, i.e. δ(t−Tt₀), is outside the synthesis window 221. At the sametime, another Dirac pulse 224 of the pulse train, i.e. δ(t−Tt₀+L) attime instant t=Tt₀−L, is picked up by the synthesis window. In otherwords, the input Dirac pulse 212 is not delayed to a T times later timeinstant, but it is moved forward to a time instant that lies before theinput Dirac pulse 212. The final effect on the audio signal is theoccurrence of a pre-echo at a time distance of the scale of the ratherlong transposer windows, i.e. at a time instant t=Tt₀−L which isL−(T−1)t₀ earlier than the input Dirac pulse 212.

The principle of the solution proposed by the present invention isdescribed in reference to FIG. 3. FIG. 3 illustrates ananalysis/synthesis scenario 300 similar to FIG. 2. The upper graph 310shows the input to the analysis stage with the analysis window 311, andthe lower graph 320 shows the output of the synthesis stage with thesynthesis window 321. The basic idea of the invention is to adapt theDFT size so as to avoid pre-echoes. This may be achieved by setting thesize M of the DFT such that no unwanted Dirac pulse images from theresulting pulse train are picked up by the synthesis window. The size ofthe DFT transform 301 is increased to M=FL, where L is the length of thewindow function 302 and the factor F is a frequency domain oversamplingfactor. In other words, the size of the DFT transform 301 is selected tobe larger than the window size 302. In particular, the size of the DFTtransform 301 may be selected to be larger than the window size 302 ofthe synthesis window. Due to the increased length 301 of the DFTtransform, the period of the pulse train comprising the Dirac pulses322, 324 is FL. By selecting a sufficiently large value of F, i.e. byselecting a sufficiently large frequency domain oversampling factor,undesired contributions to the pulse stretch can be cancelled. This isshown in FIG. 3, where the Dirac pulse 324 at time instant t=Tt₀−FL liesoutside the synthesis window 321. Therefore, the Dirac pulse 324 is notpicked up by the synthesis window 321 and by consequence, pre-echoes canbe avoided.

It should be noted that in a preferred embodiment the synthesis windowand the analysis window have equal “nominal” lengths. However, whenusing implicit resampling of the output signal by discarding orinserting samples in the frequency bands of the transform or filterbank, the synthesis window size will typically be different from theanalysis size, depending on the resampling or transposition factor.

The minimum value of F, i.e. the minimum frequency domain oversamplingfactor, can be deduced from FIG. 3. The condition for not picking upundesired Dirac pulse images may be formulated as follows: For any inputpulse δ(t−t₀) at position

${t = {t_{0} < \frac{L}{2}}},$

i.e. for any input pulse comprised within the analysis window 311, theundesired image δ(t−Tt₀+FL) at time instant t=Tt₀−FL must be located tothe left of the left edge of the synthesis window at

$t = {- {\frac{L}{2}.}}$

Equivalently, the condition

${{T\frac{L}{2}} - {FL}} \leq {- \frac{L}{2}}$

must be met, which leads to the rule

$\begin{matrix}{F \geq {\frac{T + 1}{2}.}} & (3)\end{matrix}$

As can be seen from formula (3), the minimum frequency domainoversampling factor F is a function of the transposition/time-stretchingfactor T. More specifically, the minimum frequency domain oversamplingfactor F is proportional to the transposition/time-stretching factor T.

By repeating the line of thinking above for the case where the analysisand synthesis windows have different lengths one obtains a more generalformula. Let L_(A) and L_(S) be the lengths of the analysis andsynthesis windows, respectively, and let M be the DFT size employed. Therule extending formula (3) is then

$\begin{matrix}{M \geq {\frac{{TL}_{A} + L_{S}}{2}.}} & (4)\end{matrix}$

That this rule indeed is an extension of (3) can be verified byinserting M=FL, and L_(A)=L_(S)=L in (4) and dividing by L on both sideof the resulting equation.

The above analysis is performed for a rather special model of atransient, i.e. a Dirac pulse. However, the reasoning can be extended toshow that when using the above described time-stretching scheme, inputsignals which have a near flat spectral envelope and which vanishoutside a time interval [a, b] will be stretched to output signals whichare small outside the interval [Ta,Tb]. It can also be checked bystudying spectrograms of real audio and/or speech signals thatpre-echoes disappear in the stretched signals when the above describedrule for selecting an appropriate frequency domain oversampling factoris respected. A more quantitative analysis also reveals that pre-echoesare still reduced when using frequency domain oversampling factors whichare slightly inferior to the value imposed by the condition of formula(3). This is due to the fact that typical window functions v_(s)(n) aresmall near their edges, thereby attenuating undesired pre-echoes whichare positioned near the edges of the window functions.

In summary, the present invention teaches a new way to improve thetransient response of frequency domain harmonic transposers, ortime-stretchers, by introducing an oversampled transform, where theamount of oversampling is a function of the transposition factor chosen.

In the following, the application of harmonic transposition according tothe invention in audio decoders is described in further detail. A commonuse case for a harmonic transposer is in an audio/speech codec systememploying so-called bandwidth extension or high frequency regeneration(HFR). It should be noted that even though reference may be made toaudio coding, the described methods and systems are equally applicableto speech coding and in unified speech and audio coding (USAC).

In such HFR systems the transposer may be used to generate a highfrequency signal component from a low frequency signal componentprovided by the so-called core decoder. The envelope of the highfrequency component may be shaped in time and frequency based on sideinformation conveyed in the bitstream.

FIG. 4 illustrates the operation of an HFR enhanced audio decoder. Thecore audio decoder 401 outputs a low bandwidth audio signal which is fedto an up-sampler 404 which may be required in order to produce a finalaudio output contribution at the desired full sampling rate. Suchup-sampling is required for dual rate systems, where the band limitedcore audio codec is operating at half the external audio sampling rate,while the HFR part is processed at the full sampling frequency.Consequently, for a single rate system, this up-sampler 404 is omitted.The low bandwidth output of 401 is also sent to the transposer or thetransposition unit 402 which outputs a transposed signal, i.e. a signalcomprising the desired high frequency range. This transposed signal maybe shaped in time and frequency by the envelope adjuster 403. The finalaudio output is the sum of low bandwidth core signal and the envelopeadjusted transposed signal.

As outlined in the context of FIG. 4, the core decoder output signal maybe up-sampled as a pre-processing step by a factor 2 in thetransposition unit 402. A transposition by a factor T results in asignal having T times the length of the un-transposed signal, in case oftime-stretching. In order to achieve the desired pitch-shifting orfrequency transposition to T times higher frequencies, down-sampling orrate-conversion of the time-stretched signal is subsequently performed.As mentioned above, this operation may be achieved through the use ofdifferent analysis and synthesis strides in the phase vocoder.

The overall transposition order may be obtained in different ways. Afirst possibility is to up-sample the decoder output signal by thefactor 2 at the entrance to the transposer as pointed out above. In suchcases, the time-stretched signal would need to be down-sampled by afactor T, in order to obtain the desired output signal which isfrequency transposed by a factor T. A second possibility would be toomit the pre-processing step and to directly perform the time-stretchingoperations on the core decoder output signal. In such cases, thetransposed signals must be down-sampled by a factor T/2 to retain theglobal up-sampling factor of 2 and in order to achieve frequencytransposition by a factor T. In other words, the up-sampling of the coredecoder signal may be omitted when performing a down-sampling of theoutput signal of the transposer 402 of T/2 instead of T. It should benoted, however, that the core signal still needs to be up-sampled in theup-sampler 404 prior to combining the signal with the transposed signal.

It should also be noted that the transposer 402 may use severaldifferent integer transposition factors in order to generate the highfrequency component. This is shown in FIG. 5 which illustrates theoperation of a harmonic transposer 501, which corresponds to thetransposer 402 of FIG. 4, comprising several transposers of differenttransposition order or transposition factor T. The signal to betransposed is passed to the bank of individual transposers 501-2, 501-3,. . . , 501-T_(max) having orders of transposition T=2, 3, . . . ,T_(max), respectively. Typically a transposition order T_(max)=4suffices for most audio coding applications. The contributions of thedifferent transposers 501-2, 501-3, . . . , 501-T_(max) are summed in502 to yield the combined transposer output. In a first embodiment, thissumming operation may comprise the adding up of the individualcontributions. In another embodiment, the contributions are weightedwith different weights, such that the effect of adding multiplecontributions to certain frequencies is mitigated. For instance, thethird order contribution may be added with a lower gain than the secondorder contribution. Finally, the summing unit 502 may add thecontributions selectively depending on the output frequency. Forinstance, the second order transposition may be used for a first lowertarget frequency range, and the third order transposition may be usedfor a second higher target frequency range.

FIG. 6 illustrates the operation of a harmonic transposer, such as oneof the individual blocks of 501, i.e. one of the transposers 501-T oftransposition order T. An analysis stride unit 601 selects successiveframes of the input signal which is to be transposed. These frames aresuper-imposed, e.g. multiplied, in an analysis window unit 602 with ananalysis window. It should be noted that the operations of selectingframes of an input signal and multiplying the samples of the inputsignal with an analysis window function may be performed in a uniquestep, e.g. by using a window function which is shifted along the inputsignal by the analysis stride. In the analysis transformation unit 603,the windowed frames of the input signal are transformed into thefrequency domain. The analysis transformation unit 603 may e.g. performa DFT. The size of the DFT is selected to be F times greater than thesize L of the analysis window, thereby generating M=F*L complexfrequency domain coefficients. These complex coefficients are altered inthe non-linear processing unit 604, e.g. by multiplying their phase withthe transposition factor T. The sequence of complex frequency domaincoefficients, i.e. the complex coefficients of the sequence of frames ofthe input signal, may be viewed as subband signals. The combination ofanalysis stride unit 601, analysis window unit 602 and analysistransformation unit 603 may be viewed as a combined analysis stage oranalysis filter bank.

The altered coefficients or altered subband signals are retransformedinto the time domain using the synthesis transformation unit 605. Foreach set of altered complex coefficients, this yields a frame of alteredsamples, i.e. a set of M altered samples. Using the synthesis windowunit 606, L samples may be extracted from each set of altered samples,thereby yielding a frame of the output signal. Overall, a sequence offrames of the output signal may be generated for the sequence of framesof the input signal. This sequence of frames is shifted with respect toone another by the synthesis stride in the synthesis stride unit 607.The synthesis stride may be T times greater than the analysis stride.The output signal is generated in the overlap-add unit 608, where theshifted frames of the output signal are overlapped and samples at thesame time instant are added. By traversing the above system, the inputsignal may be time-stretched by a factor T, i.e. the output signal maybe a time-stretched version of the input signal.

Finally, the output signal may be contracted in time using thecontracting unit 609. The contracting unit 609 may perform a samplingrate conversion of order T, i.e. it may increase the sampling rate ofthe output signal by a factor T, while keeping the number of samplesunchanged. This yields a transposed output signal, having the samelength in time as the input signal but comprising frequency componentswhich are up-shifted by a factor T with respect to the input signal. Thecombining unit 609 may also perform a down-sampling operation by afactor T, i.e. it may retain only every T^(th) sample while discardingthe other samples. This down-sampling operation may also be accompaniedby a low pass filter operation. If the overall sampling rate remainsunchanged, then the transposed output signal comprises frequencycomponents which are up-shifted by a factor T with respect to thefrequency components of the input signal.

It should be noted that the contracting unit 609 may perform acombination of rate-conversion and down-sampling. By way of example, thesampling rate may be increased by a factor 2. At the same time thesignal may be down-sampled by a factor T/2. Overall, such combination ofrate-conversion and down-sampling also leads to an output signal whichis a harmonic transposition of the input signal by a factor T. Ingeneral, it may be stated that the contracting unit 609 performs acombination of rate conversion and/or down-sampling in order to yield aharmonic transposition by the transposition order T. This isparticularly useful when performing harmonic transposition of the lowbandwidth output of the core audio decoder 401. As outlined above, suchlow bandwidth output may have been down-sampled by a factor 2 at theencoder and may therefore require up-sampling in the up-sampling unit404 prior to merging it with the reconstructed high frequency component.Nevertheless, it may be beneficial for reducing computation complexityto perform harmonic transposition in the transposition unit 402 usingthe “non-up-sampled” low bandwidth output. In such cases, thecontracting unit 609 of the transposition unit 402 may perform arate-conversion of order 2 and thereby implicitly perform the requiredup-sampling operation of the high frequency component. By consequence,transposed output signals of order T are down-sampled in the contractingunit 609 by the factor T/2.

In the case of multiple parallel transposers of different transpositionorders such as shown in FIG. 5, some transformation or filter bankoperations may be shared between different transposers 501-2, 501-3, . .. , 501-T_(max). The sharing of filter bank operations may be donepreferably for the analysis in order to obtain more effectiveimplementations of transposition units 402. It should be noted that apreferred way to resample the outputs from different tranposers is todiscard DFT-bins or subband channels before the synthesis stage. Thisway, resampling filters may be omitted and complexity may be reducedwhen performing an inverse DFT/synthesis filter bank of smaller size.

As just mentioned, the analysis window may be common to the signals ofdifferent transposition factors. When using a common analysis window, anexample of the stride of windows 700 applied to the low band signal isdepicted in FIG. 7. FIG. 7 shows a stride of analysis windows 701, 702,703 and 704, which are displaced with respect to one another by theanalysis hop factor or analysis time stride Δt_(a).

An example of the stride of windows applied to the low band signal, e.g.the output signal of the core decoder, is depicted in FIG. 8( a). Thestride with which the analysis window of length L is moved for eachanalysis transform is denoted Δt_(a). Each such analysis transform andthe windowed portion of the input signal is also referred to as a frame.The analysis transform converts/transforms the frame of input samplesinto a set of complex FFT coefficient. After the analysis transform, thecomplex FFT coefficients may be transformed from Cartesian to polarcoordinates. The suite of FFT coefficients for subsequent frames makesup the analysis subband signals. For each of the transposition factorsT=2, 3, . . . , T_(max) used, the phase angles of the FFT coefficientsare multiplied by the respective transposition factor T and transformedback to Cartesian coordinates. Hence, there will be a different set ofcomplex FFT coefficients representing a particular frame for everytransposition factor T. In other words, for each of the transpositionfactors T=2, 3, . . . , T_(max) and for each frame, a separate set ofFFT coefficients is determined. By consequence, for every transpositionorder T a different set of synthesis subband signals Y(t_(s) ^(k),Ω_(m))is generated.

In the synthesis stages, the synthesis strides Δt_(s) of the synthesiswindows are determined as a function of the transposition order T usedin the respective transposer. As outlined above, the time-stretchoperation also involves time stretching of the subband signals, i.e.time stretching of the suite of frames. This operation may be performedby choosing a synthesis hop factor or synthesis stride Δt_(s) which isincreased over the analysis stride Δt_(a) by a factor T. Consequently,the synthesis stride Δt_(sT) for the transposer of order T is given byΔt_(sT)=TΔt_(a). FIGS. 8 (b) and 8 (c) show the synthesis stride Δt_(sT)of synthesis windows for the transposition factors T=2 and T=3,respectively, where Δt_(s2)=2Δt_(a) and Δt_(s3)=3Δt_(a).

FIG. 8 also indicates the reference time t_(r) which has been“stretched” by a factor T=2 and T=3 in FIGS. 8 (b) and 8 (c) compared toFIG. 8( a), respectively. However, at the outputs this reference timet_(r) needs to be aligned for the two transposition factors. To alignthe output, the third order transposed signal, i.e. FIG. 8( c), needs tobe down-sampled or rate-converted with the factor 3/2. Thisdown-sampling leads to a harmonic transposition in respect to the secondorder transposed signal. FIG. 9 illustrates the effect of there-sampling on the synthesis stride of windows for T=3. If it is assumedthat the analysed signal is the output signal of a core decoder whichhas not been up-sampled, then the signal of FIG. 8 (b) has beeneffectively frequency transposed by a factor 2 and the signal of FIG. 8(c) has been effectively frequency transposed by a factor 3.

In the following, the aspect of time alignment of transposed sequencesof different transposition factors when using common analysis windows isaddressed. In other words, the aspect of aligning the output signals offrequency transposers employing a different transposition order isaddressed. When using the methods outlined above, Dirac-functionsδ(t−t₀) are time-stretched, i.e. moved along the time axis, by theamount of time given by the applied transposition factor T. In order toconvert the time-stretching operation into a frequency shiftingoperation, a decimation or down-sampling using the same transpositionfactor T is performed. If such decimation by the transposition factor ortransposition order T is performed on the time-stretched Dirac-functionδ(t−Tt₀), the down-sampled Dirac pulse will be time aligned with respectto the zero-reference time 710 in the middle of the first analysiswindow 701. This is illustrated in FIG. 7.

However, when using different orders of transposition T, the decimationswill result in different offsets for the zero-reference, unless thezero-reference is aligned with “zero” time of the input signal. Byconsequence, a time offset adjustment of the decimated transposedsignals need to be performed, before they can be summed up in thesumming unit 502. As an example, a first transposer of order T=3 and asecond transposer of order T=4 are assumed. Furthermore, it is assumedthat the output signal of the core decoder is not up-sampled. Then thetransposer decimates the third order time-stretched signal by a factor3/2, and the fourth order time-stretched signal by a factor 2. Thesecond order time-stretched signal, i.e. T=2, will just be interpretedas having a higher sampling frequency compared to the input signal, i.e.a factor 2 higher sampling frequency, effectively making the outputsignal pitch-shifted by a factor 2.

It can be shown that in order to align the transposed and down-sampledsignals, time offsets by

$\frac{\left( {T - 2} \right)L}{4}$

need to be applied to the transposed signals before decimation, i.e. forthe third and fourth order transpositions, offsets of

$\frac{L}{4}\mspace{14mu} {and}\mspace{14mu} \frac{L}{2}$

have to be applied respectively. To verify this in a concrete example,the zero-reference for a second order time-stretched signal will beassumed to correspond to time instant or sample

$\frac{L}{2},$

i.e. to the zero-reference 710 in FIG. 7. This is so, because nodecimation is used. For a third order time-stretched signal, thereference will translate to

${{\frac{L}{2}\left( \frac{2}{3} \right)} = \frac{L}{3}},$

due to down-sampling by a factor of 3/2. If the time offset according tothe above mentioned rule is added before decimation, the reference willtranslate into

${\left( {\frac{L}{2} + \frac{L}{4}} \right)\left( \frac{2}{3} \right)} = {\frac{L}{2}.}$

This means that the reference of the down-sampled transposed signal isaligned with the zero-reference 710. In a similar manner, for the fourthorder transposition without offset the zero-reference corresponds to

${{\frac{L}{2}\left( \frac{1}{2} \right)} = \frac{L}{4}},$

but when using the proposed offset, the reference translates into

${{\left( {\frac{L}{2} + \frac{L}{2}} \right)\left( \frac{1}{2} \right)} = \frac{L}{2}},$

which again is aligned with the 2^(nd) order zero-reference 710, i.e.the zero-reference for the transposed signal using T=2.

Another aspect to be considered when simultaneously using multipleorders of transposition relates to the gains applied to the transposedsequences of different transposition factors. In other words, the aspectof combining the output signals of transposers of differenttransposition order may be addressed. There are two principles whenselecting the gain of the transposed signals, which may be consideredunder different theoretical approaches. Either, the transposed signalsare supposed to be energy conserving, meaning that the total energy inthe low band signal which subsequently is transposed to constitute afactor-T transposed high band signal is preserved. In this case theenergy per bandwidth should be reduced by the transposition factor Tsince the signal is stretched by the same amount T in frequency.However, sinusoids, which have their energy within an infinitesimallysmall bandwidth, will retain their energy after transposition. This isdue to the fact that in the same way as a Dirac pulse is moved in timeby the transposer when time-stretching, i.e. in the same way that theduration in time of the pulse is not changed by the time-stretchingoperation, a sinusoidal is moved in frequency when transposing, i.e. theduration in frequency (in other words the bandwidth) is not changed bythe frequency transposing operation. I.e. even though the energy perbandwidth is reduced by T, the sinusoidal has all its energy in onepoint in frequency so that the point-wise energy will be preserved.

The other option when selecting the gain of the transposed signals is tokeep the energy per bandwidth after transposition. In this case,broadband white noise and transients will display a flat frequencyresponse after transposition, while the energy of sinusoids willincrease by a factor T.

A further aspect of the invention is the choice of analysis andsynthesis phase vocoder windows when using common analysis windows. Itis beneficial to carefully choose the analysis and synthesis phasevocoder windows, i.e. v_(a)(n) and v_(s)(n). Not only should thesynthesis window v_(s)(n) adhere to Formula 2 above, in order to allowfor perfect reconstruction. Furthermore, the analysis window v_(a)(n)should also have adequate rejection of the side lobe levels. Otherwise,unwanted “aliasing” terms will typically be audible as interference withthe main terms for frequency varying sinusoids. Such unwanted “aliasing”terms may also appear for stationary sinusoids in the case of eventransposition factors as mentioned above. The present invention proposesthe use of sine windows because of their good side lobe rejection ratio.Hence, the analysis window is proposed to be

$\begin{matrix}{{{v_{a}(n)} = {\sin \left( {\frac{\pi}{L}\left( {n + 0.5} \right)} \right)}},{0 \leq n < L}} & (4)\end{matrix}$

The synthesis windows v_(s)(n) will be either identical to the analysiswindow v_(a)(n) or given by formula (2) above if the synthesis hop-sizeΔt_(s) is not a factor of the analysis window length L, i.e. if theanalysis window length L is not integer dividable by the synthesishop-size. By way of example, if L=1024, and Δt_(s)=384, then1024/384=2.667 is not an integer. It should be noted that it is alsopossible to select a pair of bi-orthogonal analysis and synthesiswindows as outlined above. This may be beneficial for the reduction ofaliasing in the output signal, notably when using even transpositionorders T.

In the following, reference is made to FIG. 10 and FIG. 11 whichillustrate an exemplary encoder 1000 and an exemplary decoder 1100,respectively, for unified speech and audio coding (USAC). The generalstructure of the USAC encoder 1000 and decoder 1100 is described asfollows: First there may be a common pre/postprocessing consisting of anMPEG Surround (MPEGS) functional unit to handle stereo or multi-channelprocessing and an enhanced Spectral Band Replication (eSBR) unit 1001and 1101, respectively, which handles the parametric representation ofthe higher audio frequencies in the input signal and which may make useof the harmonic transposition methods outlined in the present document.Then there are two branches, one consisting of a modified Advanced AudioCoding (AAC) tool path and the other consisting of a linear predictioncoding (LP or LPC domain) based path, which in turn features either afrequency domain representation or a time domain representation of theLPC residual. All transmitted spectra for both, AAC and LPC, may berepresented in MDCT domain followed by quantization and arithmeticcoding. The time domain representation may use an ACELP excitationcoding scheme.

The enhanced Spectral Band Replication (eSBR) unit 1001 of the encoder1000 may comprise high frequency reconstruction components outlined inthe present document. In some embodiments, the eSBR unit 1001 maycomprise a transposition unit outlined in the context of FIGS. 4, 5 and6. Encoded data related to harmonic transposition, e.g. the order oftransposition used, the amount of frequency domain oversampling needed,or the gains employed, may be derived in the encoder 1000 and mergedwith the other encoded information in a bitstream multiplexer andforwarded as an encoded audio stream to a corresponding decoder 1100.

The decoder 1100 shown in FIG. 11 also comprises an enhanced SpectralBandwidth Replication (eSBR) unit 1101. This eSBR unit 1101 receives theencoded audio bitstream or the encoded signal from the encoder 1000 anduses the methods outlined in the present document to generate a highfrequency component or high band of the signal, which is merged with thedecoded low frequency component or low band to yield a decoded signal.The eSBR unit 1101 may comprise the different components outlined in thepresent document. In particular, it may comprise the transposition unitoutlined in the context of FIGS. 4, 5 and 6. The eSBR unit 1101 may useinformation on the high frequency component provided by the encoder 1000via the bitstream in order to perform the high frequency reconstruction.Such information may be the spectral envelope of the original highfrequency component to generate the synthesis subband signals andultimately the high frequency component of the decoded signal, as wellas the order of transposition used, the amount of frequency domainoversampling needed, or the gains employed.

Furthermore, FIGS. 10 and 11 illustrate possible additional componentsof a USAC encoder/decoder, such as:

-   -   a bitstream payload demultiplexer tool, which separates the        bitstream payload into the parts for each tool, and provides        each of the tools with the bitstream payload information related        to that tool;    -   a scalefactor noiseless decoding tool, which takes information        from the bitstream payload demultiplexer, parses that        information, and decodes the Huffman and DPCM coded        scalefactors;    -   a spectral noiseless decoding tool, which takes information from        the bitstream payload demultiplexer, parses that information,        decodes the arithmetically coded data, and reconstructs the        quantized spectra;    -   an inverse quantizer tool, which takes the quantized values for        the spectra, and converts the integer values to the non-scaled,        reconstructed spectra; this quantizer is preferably a companding        quantizer, whose companding factor depends on the chosen core        coding mode;    -   a noise filling tool, which is used to fill spectral gaps in the        decoded spectra, which occur when spectral values are quantized        to zero e.g. due to a strong restriction on bit demand in the        encoder;    -   a resealing tool, which converts the integer representation of        the scalefactors to the actual values, and multiplies the        un-scaled inversely quantized spectra by the relevant        scalefactors;    -   a M/S tool, as described in ISO/IEC 14496-3;    -   a temporal noise shaping (TNS) tool, as described in ISO/IEC        14496-3;    -   a filter bank/block switching tool, which applies the inverse of        the frequency mapping that was carried out in the encoder; an        inverse modified discrete cosine transform (IMDCT) is preferably        used for the filter bank tool;    -   a time-warped filter bank/block switching tool, which replaces        the normal filter bank/block switching tool when the time        warping mode is enabled; the filter bank preferably is the same        (IMDCT) as for the normal filter bank, additionally the windowed        time domain samples are mapped from the warped time domain to        the linear time domain by time-varying resampling;    -   an MPEG Surround (MPEGS) tool, which produces multiple signals        from one or more input signals by applying a sophisticated upmix        procedure to the input signal(s) controlled by appropriate        spatial parameters; in the USAC context, MPEGS is preferably        used for coding a multichannel signal, by transmitting        parametric side information alongside a transmitted downmixed        signal;    -   a signal classifier tool, which analyses the original input        signal and generates from it control information which triggers        the selection of the different coding modes; the analysis of the        input signal is typically implementation dependent and will try        to choose the optimal core coding mode for a given input signal        frame; the output of the signal classifier may optionally also        be used to influence the behaviour of other tools, for example        MPEG Surround, enhanced SBR, time-warped filterbank and others;    -   an LPC filter tool, which produces a time domain signal from an        excitation domain signal by filtering the reconstructed        excitation signal through a linear prediction synthesis filter;        and    -   an ACELP tool, which provides a way to efficiently represent a        time domain excitation signal by combining a long term predictor        (adaptive codeword) with a pulse-like sequence (innovation        codeword).

FIG. 12 illustrates an embodiment of the eSBR units shown in FIGS. 10and 11. The eSBR unit 1200 will be described in the following in thecontext of a decoder, where the input to the eSBR unit 1200 is the lowfrequency component, also known as the low band, of a signal.

In FIG. 12 the low frequency component 1213 is fed into a QMF filterbank, in order to generate QMF frequency bands. These QMF frequencybands are not to be mistaken with the analysis subbands outlined in thisdocument. The QMF frequency bands are used for the purpose ofmanipulating and merging the low and high frequency component of thesignal in the frequency domain, rather than in the time domain. The lowfrequency component 1214 is fed into the transposition unit 1204 whichcorresponds to the systems for high frequency reconstruction outlined inthe present document. The transposition unit 1204 generates a highfrequency component 1212, also known as highband, of the signal, whichis transformed into the frequency domain by a QMF filter bank 1203.Both, the QMF transformed low frequency component and the QMFtransformed high frequency component are fed into a manipulation andmerging unit 1205. This unit 1205 may perform an envelope adjustment ofthe high frequency component and combines the adjusted high frequencycomponent and the low frequency component. The combined output signal isre-transformed into the time domain by an inverse QMF filter bank 1201.

Typically the QMF filter bank 1202 comprise 32 QMF frequency bands. Insuch cases, the low frequency component 1213 has a bandwidth of f_(s)/4,where f_(s)/2 is the sampling frequency of the signal 1213. The highfrequency component 1212 typically has a bandwidth of f_(s)/2 and isfiltered through the QMF bank 1203 comprising 64 QMF frequency bands.

In the present document, a method for harmonic transposition has beenoutlined. This method of harmonic transposition is particularly wellsuited for the transposition of transient signals. It comprises thecombination of frequency domain oversampling with harmonic transpositionusing vocoders. The transposition operation depends on the combinationof analysis window, analysis window stride, transform size, synthesiswindow, synthesis window stride, as well as on phase adjustments of theanalysed signal. Through the use of this method undesired effects, suchas pre- and post-echoes, may be avoided. Furthermore, the method doesnot make use of signal analysis measures, such as transient detection,which typically introduce signal distortions due to discontinuities inthe signal processing. In addition, the proposed method only has reducedcomputational complexity. The harmonic transposition method according tothe invention may be further improved by an appropriate selection ofanalysis/synthesis windows, gain values and/or time alignment.

1. A system for transposing an input audio signal by a transpositionfactor T, the system comprising: a parser for extracting a frame of Ltime-domain samples of the input signal using an analysis window oflength L, a transformer for converting the L time-domain samples into Mcomplex frequency-domain coefficients; a nonlinear processing unit foraltering a phase of the frequency-domain complex coefficients using thetransposition factor T; a transformer for converting the alteredfrequency-domain coefficients into M altered time-domain samples; and agenerator for creating a frame of L time-domain output samples from theM altered time-domain samples using a synthesis window; wherein M=F*L,with F being a frequency domain oversampling factor which is based onthe transposition factor T.
 2. The system of claim 1, wherein theoversampling factor F is greater or equal to (T+1)/2.
 3. The system ofclaim 1, wherein the altering of the phase comprises multiplying thephase by the transposition factor T.
 4. The system of claim 1, whereinthe analysis window has a length L with zero padding by additional(F−1)*L zeros.
 5. The system of claim 1, wherein the transformer forconverting the altered frequency-domain coefficients comprises ananalysis transformation unit of size M for transforming the Ltime-domain samples into M complex frequency-domain coefficients.
 6. Thesystem of claim 1, further comprising: an analysis stride unit forshifting the analysis window by an analysis stride along the inputsignal to generate successive frames of the input signal; a synthesisstride unit for shifting successive frames of L time-domain outputsamples by a synthesis stride; and an overlap-add unit for overlappingand adding the successive shifted frames of L time-domain output samplesto generate an output signal.
 7. The system of claim 6, furthercomprising a contraction unit for increasing the sampling rate of theoutput signal by the transposition order T to yield a transposed outputsignal.
 8. The system of claim 7, wherein the synthesis stride is Ttimes the analysis stride.
 9. A method for transposing an input audiosignal by a transposition factor T, the method comprising: extracting aframe of L time-domain samples of the input signal using an analysiswindow of length L, transforming the L time-domain samples into Mcomplex frequency-domain coefficients, altering a phase of thefrequency-domain complex coefficients using the transposition factor T;transforming the altered frequency-domain coefficients into M alteredtime-domain samples; and generating a frame of L time-domain outputsamples from the M altered time-domain samples using a synthesis window;wherein M=F*L, with F being a frequency domain oversampling factor whichis based on the transposition factor T.
 10. The method of claim 9,wherein transforming the L time-domain samples into M complexfrequency-domain coefficients is performing one of a Fourier Transform,a Fast Fourier Transform, a Discrete Fourier Transform, a WaveletTransform.
 11. The method of claim 9, wherein the oversampling factor Fis greater or equal to (T+1)/2.
 12. The method of claim 9, wherein theinput signal comprises a low frequency component of an audio signal. 13.A non-transitory computer readable medium comprising instructions forexecution on a processor and for performing the method of claim 9 whencarried out on a computing device.